Safari browsing history

Top of the screen while in Safari, hit that open-book icon (i.e. the bookmarks tab). There are your bookmarks, and a tab for "History" Scroll to the bottom of History and delete all. Or delete individual items.

3rd party browser all have their own setup, so that varies.

You can also go to Settings, scroll down to Safari, tap on Safari, and then clean the Cache, history etc...